Statistical uncertainty quantification for multireference covariant density functional theory

We present a theoretical framework to quantify statistical uncertainties in covariant density functional theory (CDFT) for both nuclear matter and finite nuclei, based on a relativistic point-coupling energy density functional (EDF). By sampling approximately one million parameter sets, with nine parameters varied around their values in the PC-PK1 functional, we construct a probability density function for nuclear matter properties. Incorporating empirical values of nuclear matter at saturation density and those of predictions from chiral nuclear forces, and measured $B(E2)$ values of finite nuclei, we infer posterior distributions for the model parameters within a Bayesian framework. These posterior distributions are then propagated to the low-lying states of finite nuclei using the newly developed subspace-projected (SP)-CDFT approach, in which the wave functions of target EDF parameter sets are expanded in a subspace spanned by low-lying states obtained from a set of training parameterizations. We find that the observables of low-lying states in deformed nuclei $^{150}$Nd and $^{150}$Sm are well reproduced once statistical uncertainties are taken into account. In contrast, those of near spherical nuclei $^{136}$Xe and $^{136}$Ba remain difficult to describe within the present framework, a limitation that is expected to be alleviated by extending the model space to include quasiparticle excitations.